Currently, fixed mortgage rates are $6\%$ for a $30-$year mortgage. You checked and found a $3/1$ adjustable$-$rate mortgage with a $30-$year amortization of $5\mathrm{.}0\%.$ The terms of the adjustable$-$rate mortgage are:

Index Rate: $4\%$

Margin: $2\%$

Annual cap $1\%$

After three years, the index rate is now $7\%,$ what is your new mortgage rate?